Its transform to the f–scheme
for \(\Gamma ^3 \chi _4^{\rm f-h}\)  is given in Eq. (8.6) there, to eliminate the term of \(O(\pi \nu ^2p_\infty ^6)\) .Eq. (7.24) of [1]} contains typos. Both \(a_{\rm 5 PN}\)  and \(b_{\rm 5 PN}\) 
need an additional factor \(p_\infty ^2\) . Otherwise Eq. (8.2) will not hold.
One has
\(\Gamma ^3 \chi _4^{\rm nonloc, h} &=& \nu \eta ^8 p_\infty ^4 \pi \Biggl \lbrace - \frac{63}{4} - \frac{37}{5}\ln \left(\frac{p_\infty }{2}\right)+ \eta ^2 p_\infty ^2 \Biggl [ - \frac{2753}{1120} - \frac{1357}{280} \ln \left(\frac{p_\infty }{2}\right) + \frac{63}{20} \nu \Biggr ]\Biggr \rbrace .\) 
